Teachers' Conceptions of Mathematics and Mathematics Education. A Report from the Urban Mathematics Collaborataive Documentation Project.

Middleton, James A.; And Others

This paper reports the opinions of urban mathematics teachers concerning five areas of school mathematics: mathematics, mathematics teaching, recommended changes in mathematics education, mathematics education, and schooling. Of the 490 secondary mathematics teachers surveyed, 47 percent were frequent participants in the Urban Mathematics Collaborative (UMC), 41 percent were occasional participants, and 8 percent had never participated. An additional group of 40 UMC teachers were asked to respond to corresponding items on the Diary of Professional Relationships survey to provide more personalized and diverse information and to validate findings from group data. Responses indicate that teachers view mathematics primarily as thinking. They want their students to think critically, to understand and use mathematics effectively, and to appreciate the value and beauty of mathematics. Most teachers seemed to hold an eclectic view of mathematics, although one cluster group viewed it as dynamic and changing, while another group viewed it more as a fixed body of skills and rules. These conceptions of mathematics related to the teachers' conceptions of mathematics teaching, recommended changes, mathematics education, and schooling. Frequent participants in the UMC held more favorable views toward recommended changes in mathematics education than the others. The results of this survey are discussed in relation to the UMC's efforts to empower teachers and reduce their feelings of isolation and burnout. Results of the survey are summarized in three tables and one figure. Forty-one references and seven appendixes (with over 100 tables) are included. (CJS)